Root structures of the Yablonskii-Vorob'ev polynomial hierarchy have been studied before [1]}, [2]}, [3]}, [4]}, [5]}. Regarding the zero root, its multiplicity in \(Q_{N}(z)\) , \(Q_{N}^{[2]}(z)\)  and \(Q_{N}^{[3]}(z)\)  was presented in [2]}, [3]}. Generalizing those results, we have the following theorem.
